Methods and electronic devices for obtaining information on a battery pack

ABSTRACT

Methods and electronic devices for estimating state of charge (SOC) of a battery pack. Various embodiments provide a model comprising an (electrical) equivalent circuit model, an electrochemical (thermal) model, and a (convective) thermal model. The model estimates parameters pertaining to each cell of the battery pack individually, and determines the variations in the values of the parameters among each of the cells of the battery pack. The parameters include capacity, temperature current, voltage, and SOC. The parameters are computed based on at current drawn by the battery pack, electrochemical parameters, thermal parameters, and cell internal and connection resistances of the individual cells. Various embodiments compute battery pack uptime, chargeable capacity of the battery pack and SOC of the battery pack, based on the values of the parameters.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is based on and claims priority under 35 U.S.C. § 119to Indian Provisional Patent Application No. 202041010259, filed on Mar.10, 2020, in the Indian Patent Office, and Indian Complete PatentApplication No. 202041010259, filed on Nov. 30, 2020, in the IndianPatent Office the disclosures of which are incorporated by referenceherein in their entireties.

BACKGROUND Field

The disclosure relates to Battery Management Systems (BMS), and forexample, to methods and electronic devices for accurately estimatingState of Charge (SOC), uptime and capacity of a battery pack.

Description of Related Art

A battery pack comprises a plurality of cells, wherein each cell can beconnected to other cells in series or parallel. Currently, coulombcounting is being used for determining the State of Charge (SOC) of thebattery pack. Coulomb counting typically considers the input current atthe battery pack level, assuming that the current distribution acrossall cells of the battery pack is uniform and capacities of all cells inthe battery pack are same.

These considerations, however, can introduce errors in the estimation ofthe SOC of the battery pack. This is because it is likely that there arevariations in parameters such as capacities, resistances (internal andconnection), temperatures (ambient and surface), SOC, and so on, amongstthe cells of the battery pack. The variations in the parameters aremagnified with increasing number of charge-discharge cycles. During themanufacturing of the battery pack, variations (tolerances) can beintroduced in the components at the cell level. This can lead to furthervariations in the parameters. The cell-to-cell variations in theparameters lead to deviations in current flowing through each cell andvoltage across the terminals of each cell, which can further introducevariations in the SOC and the capacities (State of Health (SOH)) amongstthe cells of the battery pack.

The connectors, bolts and nuts, cables, and bus bars contribute to theoverall resistance and impedance of the battery pack. These resistancescan divert current, divide voltage, generate heat, and introduceadditional factors (which may be non-linear) used for estimating the SOCof the battery pack. The additional impedances can be distributednon-uniformly across the cells of the battery pack. Therefore, theadditional impedances can impact the accuracy of estimation of the SOCand the capacity of the battery pack. The cell-to-cell thermalvariations, based on locations of the cells (a cell located in a corneris likely to have a lesser surface and ambient temperatures compared toa cell located in a center of the battery pack), can trigger voltage andcapacity variations. The voltage and capacity variations can leads toredistribution of current amongst the cells of the battery pack, therebyaffecting the distribution of charge across the individual cells, andSOC of individual cells in the battery pack and/or the SOC of thebattery pack.

If multiple cells in the battery pack are connected in series, it isexpected that the same current is passing through each of the cells.However, due to cell-to-cell variations in the parameters, the samecurrent passing through all the cells may not translate into anequivalent range of SOC. There can also be cell-to-cell variations involtage drop (even though the cells are connected in series). Similarly,if the multiple cells in the battery pack are connected in parallel, itis expected that the voltage across the terminals of each of the cellsis same due to spontaneous internal balance. However, the internalbalance may be affected by factors such as variations in cell internalresistance, which in turn affects the current distribution in the(parallel) branches (in which the cells are located).

In other existing methods, the remaining capacity and the chargeablecapacity of the battery pack is determined based on the cell having thelowest capacity. This is because the cell having the lowest capacity isexpected to discharge first, and when the cell (having the lowestcapacity) discharges, it is considered that the cells connected inseries with the discharged cell have ceased to function. Thisconsideration can also lead to erroneous estimation of the SOC and thebattery pack uptime, because there are conditions wherein a cell havinghigher capacity can discharge faster than the cell having the lowestcapacity. If the cell having the lowest capacity is connected inparallel with other cells and is having a high internal resistance, thecurrent flowing through the cell will be the lowest amongst the currentsflowing through the other cells. Also, if the cell having the lowestcapacity is connected in series with other cells, and if the busbarconnection resistance of the cell is lower compared to the other cells,then a same amount of charge (current) passing through all cells canlead to lower voltage drop or SOC at the cell (having the lowestcapacity). This will reduce the rate of discharge of the cell and expandthe uptime of the cell, compared to the other cells having a highercapacity.

The errors in the estimations of the remaining capacity and the SOC ofthe battery pack can mislead a user. The impact of these errors isparticularly significant at the end of the discharge cycles. Considerthat the actual SOC of the battery pack is 1% and the SOC of the batteryis computed as 12%. In this scenario, the user, while expecting thebattery pack to function normally for a certain period of time (orpreparing to charge the battery pack), may experience a sudden drop inthe SOC of the battery pack and an unexpected/early shutdown of theequipment hosting the battery pack. Therefore, erroneous estimation ofthe remaining capacity and the SOC of the battery pack may impact thereliability of the battery pack, and consequently the user experience.

SUMMARY

Embodiments of the disclosure disclose methods and electronic devicesfor providing a model for more accurately estimating at least one ofuptime of a battery pack, chargeable capacity of the battery pack, Stateof Charge (SOC) of the battery pack, voltage of the battery pack,temperature of the battery pack, and remaining capacity of the batterypack.

Embodiments of the disclosure perform the estimations using at least oneof an equivalent circuit model, an electrochemical model, and a thermalmodel, wherein the equivalent circuit model, the electrochemical model,and the thermal model are coupled to each other.

Embodiments of the disclosure perform estimation in real time (online)or prior to termination of every discharge cycle, wherein the estimationis performed based on cell-to-cell variations in at least one parametercomprising voltage of a cell, SOC of the cell, capacity of the cell,current flowing through the cell, ambient temperature of the cell, andsurface temperature of the cell.

Embodiments of the disclosure compute the voltage, current, SOC,temperature, capacity, and so on, of each of the cells of the batterypack based on at least one of current drawn by the battery pack,internal resistances, connection resistances, electrochemicalparameters, and thermal parameters.

Embodiments of the disclosure provide methods and electronic devices forproviding a model for accurately estimating uptime of a battery pack,remaining capacity of the battery pack available for discharge,chargeable capacity of the battery pack, and State of Charge (SOC) ofthe battery pack. Example embodiments include performing the estimationsbased on parameters pertaining to each of a plurality of cells in thebattery pack. In various example embodiments, the battery pack comprisesa plurality of modules connected in series, wherein each of theplurality of modules comprises a plurality of branches connected inparallel, wherein each of the plurality of branches comprises a cell.Various example embodiments include determining/identifying thevariations in the parameters amongst each of the plurality of cells (ineach of the plurality of branches) in each of the plurality of modules.In an embodiment, the parameters are SOC of a cell, capacity of thecell, voltage of the cell (branch), current flowing through the cell(branch), and ambient and surface temperatures of the cell.

Various example embodiments include determining/identifying theparameters pertaining to each of the cells based on operating currentfed to the battery pack, electrochemical parameters, thermal parameters,internal resistance of the cell, and connection resistance of the cell.In various example embodiments, the parameters can bedetermined/identified using a model, wherein the model comprises anequivalent circuit model, an electrochemical model, and thermal model,wherein the equivalent circuit model, the electrochemical model, and thethermal model are coupled with each other.

Once the parameters have been determined/identified, various exampleembodiments may include estimating/obtaining the uptime of the batterypack, the remaining capacity of the battery pack available fordischarge, the chargeable capacity of the battery pack, and the SOC ofthe battery pack. The uptime of the battery pack may be estimated basedon the uptime of a cell. The uptime of the cell may be computed based onSOC of the cell, capacity of a battery cell, and current flowing throughthe cell. The value of the uptime of the cell is lowest amongst thevalues of uptimes of the plurality of cells in the plurality of branchesof each of the plurality of modules. The remaining capacity of thebattery pack may be estimated based on remaining capacity of a cell in abranch of a module. The value of the remaining capacity of the cell maybe computed based on SOC of the cell, capacity of the cell, currentflowing through the cell, and current flowing in all branches of themodule. The value of the remaining capacity of the cell is lowestamongst the values of remaining capacities of a plurality of batterycells in the plurality of branches of each of the plurality of modules.

The chargeable capacity of the battery pack may be a chargeable capacityof a cell in a branch of a module. The value of the chargeable capacityof the cell may be computed based on SOC of the cell, capacity of thecell, current flowing through the cell, and current flowing in allbranches of the module. The value of the chargeable capacity of the cellis lowest amongst values of chargeable capacities of a plurality ofcells in the plurality of branches of each of the plurality of modules.The SOC of the battery pack may be estimated based on the remainingcapacity of the battery pack and the total capacity of the battery pack.

These and other aspects of the various example embodiments herein willbe better appreciated and understood when considered in conjunction withthe following description and the accompanying drawings. It should beunderstood, however, that the following descriptions, while indicatingvarious example embodiments and numerous specific details thereof, aregiven by way of illustration and not of limitation. Many changes andmodifications may be made within the scope of the example embodimentsherein without departing from the spirit thereof, and the embodimentsherein include all such modifications.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features and advantages of certainembodiments of the present disclosure will be more apparent from thefollowing detailed description, taken in conjunction with theaccompanying drawings, in which:

FIG. 1 is a diagram illustrating an example battery pack comprising ‘S’modules, wherein each module comprises ‘P’ branches, wherein uptime,State of Charge (SOC), and capacity of the battery pack are determinedbased on parameters pertaining to individual cells of the battery pack,according to various embodiments;

FIG. 2 is a block diagram illustrating an example Battery ManagementSystem (BMS) configured to predict capacity and SOC of a battery pack205, according to various embodiments;

FIG. 3 is a flowchart illustrating an example method for estimatingcapacity and SOC of a battery pack based on variations of parameterspertaining to battery cells of the battery pack, according to variousembodiments;

FIG. 4 is a diagram illustrating an example model for estimation ofparameters pertaining to the individual cells of the battery pack,according to various embodiments; and

FIG. 5 is a diagram illustrating an example battery pack comprisingthree modules, wherein each of the three modules comprises two branches,according to various embodiments.

DETAILED DESCRIPTION

Various example embodiments and various features and advantageousdetails thereof are explained in greater detail below with reference tothe non-limiting example embodiments illustrated in the accompanyingdrawings and described in the following disclosure. Descriptions ofwell-known components and processing techniques may be omitted so as tonot unnecessarily obscure the example embodiments herein. The examplesused herein are intended merely to facilitate an understanding of waysin which the various example embodiments herein may be practiced and tofurther enable those of skill in the art to practice the various exampleembodiments herein. Accordingly, the examples should not be construed aslimiting the scope of the various example embodiments herein.

Various example embodiments herein disclose methods and systems forproviding a model for accurately estimating at least one of State ofCharge (SOC) of a battery pack, battery pack uptime, chargeable capacityof the battery pack, voltage of the battery pack, temperature of thebattery pack, and remaining capacity of the battery pack. Variousembodiments include performing the estimations using, for example, andwithout limitation, an equivalent circuit model, an electrochemicalmodel, and a thermal model. The equivalent circuit model, theelectrochemical model, and the thermal model may be coupled to eachother. The estimation can be performed in real time (online) or prior totermination of every discharge cycle. The various example embodimentsconsider variations in at least one parameter pertaining to each cell ofthe battery pack comprising voltage of a cell, SOC of the cell, capacityof the cell, current flowing through the cell, ambient temperature ofthe cell, and surface temperature of the cell. Various embodimentsinclude computing the voltage, current, SOC, temperature, capacity, andso on, of each of the cells of the battery pack based on at least one ofcurrent drawn by the battery pack, internal and connection resistancesof the cells, electrochemical parameters, and thermal parameters.Various example embodiments include estimating the SOC of the batterypack, battery pack uptime, chargeable capacity of the battery pack, andremaining capacity of the battery pack, based on the computed values ofvoltage, current, SOC, temperature, capacity, and so on, of each of thecells of the battery pack.

Referring now to the drawings, and more particularly to FIGS. 1, 2, 3, 4and 5 , where similar reference numerals refer to corresponding featuresconsistently throughout the figures, there are shown various exampleembodiments.

FIG. 1 is a diagram illustrating an example battery pack comprising ‘S’modules, wherein each module comprises ‘P’ branches, wherein uptime,SOC, and capacity of the battery pack are determined based on parameterspertaining to individual cells of the battery pack, according to variousembodiments. As illustrated in FIG. 1 , each branch of a module includesa cell. As there are ‘S’ modules and ‘P’ branches in each module, thecells in the first module can be labeled as Cell-11, Cell-12, . . . ,and Cell-1P. Similarly, the cells in the S^(th) module can be labeled asCell-S1, Cell-S2, . . . , and Cell-SP. Each cell has an internalresistance. The resistances of the cell in the first module can belabeled as r₁₁, r₁₂, . . . , and rip. Similarly, the cells in the S^(th)module can be labeled as r_(S1), r_(S2), . . . , and r_(SP).

The modules may be referred to as units of the battery pack connected inseries. For the sake of simplicity, the charging current passing throughthe all the modules is assumed to be same. However, there can bedifferences in voltage drop across the terminals of the battery pack,e.g., the distribution of voltage amongst the modules of battery packcan be non-uniform. The voltage across the terminals of the cells in amodule can be different. There can be variations in temperature, SOC,capacity, internal resistance, busbar resistance, and so on, amongst thecells in the branches of each of the modules of battery pack. Thesevariations can cause variations in the voltage drop across the terminalsof the branches in each of the modules, and variations in the currentflowing through the different branches in each of the modules of thebattery pack. The currents flowing through the different branches of thefirst module are labeled as i₁₁, i₁₂, . . . , and i_(1P). Similarly, thecurrents flowing through the different branches of the S^(th) module canbe labeled as i_(S1), i_(S2), . . . , and i_(SP). The variations involtage and current can impact remaining and chargeable capacities ofthe battery pack.

Various example embodiments include determining/identifying theparameters pertaining to the individual cells of the battery pack suchas current (i_(jk), j→1-S, and k→1-P), SOC, capacity, voltage, ambienttemperature, and surface temperature. The parameters pertaining to eachcell of the battery pack can be determined based on operating currentfed to the battery pack (i), internal resistance of the cell, connectionresistance of the cell, electrochemical parameters and thermalparameters.

Various example embodiments include determining/obtaining the uptime ofthe battery pack, the remaining capacity of the battery pack, thechargeable capacity of the battery pack, and the SOC of the batterypack; based on variations in the parameters pertaining to the individualcells (such as cell-jk, wherein j→1-S and k→1-P) of the battery pack. Inan embodiment, the parameters are capacities of the individual cells,current passing through the individual cells (i_(jk)), and the SOC ofthe individual cells (SOC_(jk)).

The uptime of the battery pack may be computed based on SOC of a cell inthe battery pack, capacity of the battery cell, and current flowingthrough the cell. Consider that the cell is cell-jk, wherein SOC_(jk)(j→1-S and k→1-P) is the SOC of the cell, Q_(k) (j→1-S and k→1-P) is thecapacity of the cell, and i_(jk) (j→1-S and k→1-P) is the currentflowing through the cell. The uptime of a module of the battery pack, inwhich the cell-jk is located, may be:

$\begin{matrix}{{{Uptime}({module})} = {\min_{1 \leq k \leq P}\left( \frac{SOC_{jk}Q_{jk}}{i_{jk}} \right)}} & \left( {{Equation} - 1} \right)\end{matrix}$

The cell-jk is located in a branch ‘k’ of a module ‘j’. The value ofuptime of the module ‘j’ is the lowest value of uptime amongst the ‘P’values of uptimes of ‘P’ cells in the ‘P’ branches of the module ‘j’. Inthis equation (equation 1), the value of uptime of the cell in thek^(th) branch in module ‘j’ is the lowest amongst the uptimes of the ‘P’cells in the ‘P’ branches of the module ‘j’.

The uptime of the battery pack may be given as:

$\begin{matrix}{{{Uptime}({pack})} = {\min_{1 \leq i \leq S}\left\{ {\min_{1 \leq k \leq P}\left( \frac{SOC_{jk}Q_{jk}}{i_{jk}} \right)} \right\}}} & \left( {{Equation} - 2} \right)\end{matrix}$

The value of the uptime of the module ‘j’ is the lowest amongst the ‘S’values of uptimes of ‘S’ modules in the battery pack. It can beobserved, as per equation 2, that uptime of the cell-jk is the uptime ofthe battery pack, as the uptime of the cell-jk is the lowest amongst theuptimes of all cells in ‘P’ branches of each of the ‘S’ modules of thebattery pack.

The remaining capacity of the battery pack may be computed based on SOCof a cell in the battery pack, capacity of the battery cell, currentflowing through the cell and, current flowing in all branches of themodule in which the cell is located. Consider that the cell is cell-jk,wherein SOC_(jk) (j→1-S and k→1-P) is the SOC of the cell, Q_(k) (j→1-Sand k→1-P) is the capacity of the cell, and i_(jk) (j→1-S and k→1-P) isthe current flowing through the cell. The remaining capacity of a moduleof the battery pack, in which the cell-jk is located, is given as:

$\begin{matrix}{{{Rem}{{Cap}({module})}} = {{\min\limits_{1 \leq k \leq P}\left( \frac{SOC_{jk}Q_{jk}}{i_{jk}} \right)}\left( {\sum\limits_{k = 1}^{P}i_{jk}} \right)}} & \left( {{Equation} - 3} \right)\end{matrix}$

The summation represents the current flowing through the ‘P’ branches ofthe module ‘j’. The cell-jk is located in a branch ‘k’ of a module ‘j’.The value of remaining capacity of the module ‘j’ is the lowest value ofremaining capacity amongst the ‘P’ values of remaining capacities of ‘P’cells in the ‘P’ branches of the module ‘j’. In this equation the valueof remaining capacity of the cell in the k^(th) branch in module ‘j’ isthe lowest amongst the ‘P’ cells in the ‘P’ branches of the module ‘j’.The remaining capacity of the battery pack is given as:

$\begin{matrix}{{{Rem}{{Cap}({pack})}} = {\min\limits_{1 \leq j \leq S}\left\{ {{\min_{1 \leq k \leq P}\left( \frac{SOC_{jk}Q_{jk}}{i_{jk}} \right)}\left( {\sum\limits_{k = 1}^{P}i_{jk}} \right)} \right.}} & \left( {{Equation} - 4} \right)\end{matrix}$

The value of the remaining capacity of the module ‘j’ is the lowestamongst the ‘S’ values of remaining capacities of ‘S’ modules in thebattery pack. It can be observed, as per equation 4, that remainingcapacity of the cell-jk is the remaining capacity of the battery pack,as the remaining capacity of the cell-jk is the lowest amongst theremaining capacities of all cells in ‘P’ branches of each of the ‘S’modules of the battery pack.

The chargeable capacity of the battery pack may be computed based on SOCof a cell in the battery pack, capacity of the battery cell, currentflowing through the cell and, current flowing in all branches of themodule in which the cell is located. Consider that the cell is cell-jk,wherein SOC_(jk) (j→1-S and k→1-P) is the SOC of the cell, Q_(jk) (j→1-Sand k→1-P) is the capacity of the cell, and i_(jk) (j→1-S and k→1-P) isthe current flowing through the cell. The chargeable capacity of amodule of the battery pack, in which the cell-jk is located, is givenas:

$\begin{matrix}{{{Crg}{{Cap}({module})}} = {{\min\limits_{1 \leq k \leq P}\begin{pmatrix}{1 - {SOC_{jk}}} \\i_{jk}\end{pmatrix}}{Q_{jk}\left( {\sum\limits_{k = 1}^{P}i_{jk}} \right)}}} & \left( {{Equation} - 5} \right)\end{matrix}$

The summation represents the current flowing through the ‘P’ branches ofthe module ‘j’. The cell-jk is located in a branch ‘k’ of a module ‘j’.The value of chargeable capacity of the module ‘j’ is the lowest valueof chargeable capacity amongst the ‘P’ values of chargeable capacitiesof ‘P’ cells in the ‘P’ branches of the module ‘j’. In this equation thevalue of chargeable capacity of the cell in the k^(th) branch in module‘j’ is the lowest amongst the ‘P’ cells in the ‘P’ branches of themodule ‘j’. The chargeable capacity of the battery pack is given as:

$\begin{matrix}{{{Crg}{{Cap}({pack})}} = {\min\limits_{1 \leq j \leq S}\left\{ {{\min_{1 \leq k \leq P}\left( \frac{1 - {SOC_{jk}}}{i_{jk}} \right)}{Q_{jk}\left( {\sum\limits_{k = 1}^{P}i_{jk}} \right)}} \right\}}} & \left( {{Equation} - 6} \right)\end{matrix}$

The value of the chargeable capacity of the module ‘j’ is the lowestamongst the ‘S’ values of chargeable capacities of ‘S’ modules in thebattery pack. It can be observed, as per equation 4, that remainingcapacity of the cell-jk is the chargeable capacity of the battery pack,as the chargeable capacity of the cell-jk is the lowest amongst thechargeable capacities of all cells in ‘P’ branches of each of the ‘S’modules of the battery pack.

The SOC of the battery pack may be determined based on the remainingcapacity of the battery pack and the total capacity of the battery pack.The SOC of the battery pack is given as:

$\begin{matrix}{{So{C({pack})}} = \frac{\min_{1 \leq j \leq S}\left\{ {{\min_{1 \leq k \leq P}\left( \frac{SOC_{jk}Q_{jk}}{i_{jk}} \right)}\left( {\sum\limits_{k = 1}^{P}i_{jk}} \right)} \right\}}{Q_{pack}^{d}}} & \left( {{Equation} - 7} \right)\end{matrix}$

FIG. 2 is a block diagram illustrating an example Battery ManagementSystem (BMS) 200 configured to predict capacity and SOC of a batterypack 205, according to various embodiments. As illustrated in FIG. 2 ,the BMS 200 includes a Power Management Integrated Circuit (PMIC) 201.The PMIC 201 includes a processor (e.g., including processing circuitry)202, a memory 203 and a display 204. The BMS 200 is hosted in a device(not shown), which includes the battery pack 205. The battery pack 205may include a plurality of cells, wherein the plurality of cells can bearranged in series and/or parallel. In an embodiment, the battery pack205 comprises a plurality of modules connected in series, wherein eachmodule comprises a plurality of cells connected in parallel. Examples ofthe device, hosting the BMS 200, may include, but are not limited to, anelectronic device, a portable device, a mobile device/phone, a robot, anUninterrupted Power Supply (UPS), a solar panel, an electric vehicle, apersonal computer, a laptop, and so on.

The BMS 200 is configured to accurately estimate the SOC of the batterypack 205, even if there are significant variations between thecapacities of the individual cells of the battery pack 205. The BMS 200is configured to estimate remaining capacity and uptime of the batterypack 205, for determining the time period for which a user can expect tooperate the device without interruption and to avoid possible failuresduring runtime (execution of an instruction). The BMS 200 is configuredto determine the chargeable capacity of the battery pack 205. The BMS200 is configured to consider variations of SOC, temperature, capacity,voltage, current, ambient temperature, and surface temperature of eachof the individual cells of the battery pack 205, during the estimationof the SOC of the battery pack 205, the remaining capacity of thebattery pack 205, the chargeable capacity of the battery pack 205, andthe uptime of the battery pack 205.

The BMS 200 is configured to estimate the voltage drop across theterminals of each of the individual cells of the battery pack 205, andcurrent flowing through each of the individual cells. The BMS 200 isconfigured to estimate the ambient and surface temperatures of each ofthe individual cells of the battery pack 205. The BMS 200 is configuredto estimate SOC of each of the individual cells and the cell capacity ofeach of the individual cells. The estimations may, for example, beperformed based on operating current fed to the battery pack 205,electrochemical parameters, thermal parameters, internal resistances ofeach of the individual cells of the battery pack 205, and connectionresistances of each of the individual cells of the battery pack 205.

In an embodiment, the processor 202 may include various processingcircuitry and may estimate the SOC, the capacity, the voltage, thecurrent, the ambient temperature, and the surface temperature of each ofthe individual cells of the battery pack 205, using a physics basedmodel. The model comprises three sub-models, including, for example, andwithout limitation, an (electrical) equivalent circuit model, a(convective) thermal model, and a (cell reduced order) electrochemical(thermal) model. The sub-models may be fully coupled with each other.The thermal model operates at the battery pack level. Theelectrochemical model operates at the cell (cells of the battery pack205) level. Each of the sub-models can receive inputs, which includeparameters that are generated as outputs by other sub-models. Thesub-models can receive the operating current fed to the battery pack205, electrochemical parameters, thermal parameters, internalresistances of each of the individual cells of the battery pack 205, andconnection resistances of each of the individual cells of the batterypack 205, as inputs.

For a particular cell, the equivalent circuit model receives thecharging current (current fed to the battery pack 205), internalresistances of the cell, and connection resistance (contributed by theconnectors, bolts and nuts, cables, and bus bars) of the cell as inputs.The equivalent circuit model further receives the voltage of the cell,from the electrochemical model, as an input. The electrochemical modelreceives electrochemical parameters (comprising of electrode levelinformation such as length, particle radius, active material loadingcapacities, diffusion characteristics, and so on) as input. Theelectrochemical model further receives the current flowing through thecell from the equivalent circuit model, and the ambient temperature ofthe cell from the thermal model, as inputs. The thermal model receivesthermal parameters (comprising of heat transfer coefficients and coolingfluid material properties such as density, specific heat capacity, andso on) as input. The thermal model further receives the surfacetemperature of the cell from the electrochemical model as an input.

The equivalent circuit model generates the current flowing through thecell as output. The current flowing through the cell is used by theelectrochemical model as input, to predict the voltage of the cell asoutput, estimate the SOC of the cell, and estimate the capacity of thecell. The cell voltage is used as an input, by the equivalent circuitmodel, to calculate the voltage drop across the terminals and generatingthe current flowing through the cell as output. Therefore, theequivalent circuit model and the electrochemical model are coupled witheach other.

The thermal model generates the ambient temperature of the cell asoutput, which is used by the electrochemical model as input to generatethe surface temperature of the cell as output. The surface temperatureof the cell is used as input, by the thermal model, to generate theambient temperature of the cell as output. Therefore, the thermal modeland the electrochemical model are coupled with each other.

The current flowing through the individual cells, the voltage dropacross the terminals of the individual cells, the ambient temperature ofthe individual cells, surface temperature of the individual cells, actas internal input parameters and external input parameters. The chargingcurrent, internal resistances of the individual cells, connectionresistances, electrochemical parameters, and thermal parameters, are the(external) inputs of the model, which are received as inputs by thesub-models (the equivalent circuit model, the electrochemical model, andthe thermal model).

The processor 202 may estimate the SOC of the battery pack 205, theremaining capacity of the battery pack 205, the chargeable capacity ofthe battery pack 205, and the uptime of the battery pack 205, based onthe estimated values of capacity, SOC, voltage, current, and ambient andsurface temperatures of each of the individual cells of the battery pack205.

In an embodiment, the processor 202 may estimate the uptime of thebattery pack 205 based on the uptime of a cell in the battery pack 205.The uptime of the cell is determined based on SOC of a cell, capacity ofthe cell, and current flowing through the cell. The value of the uptimeof the cell is lowest amongst values of uptimes of a plurality ofbattery cells in the plurality of branches of each of the plurality ofmodules.

In an embodiment, the processor 202 may estimate the remaining capacityof the battery pack 205 based on the remaining capacity of a cellbattery pack 205. The remaining capacity of the cell is computed basedon SOC of the cell, capacity of the cell, current flowing through thecell, and current flowing in all branches of the module in which thecell is located. The value of the remaining capacity of the cell islowest amongst values of remaining capacities of a plurality of batterycells in the plurality of branches of each of the plurality of modules.In an embodiment, the processor 202 may estimate the SOC of the batterypack 205, based on the remaining capacity of the battery pack 205 andthe total capacity of the battery pack 205.

In an embodiment, the processor 202 may estimate the chargeable capacityof the battery pack 205 based on the chargeable capacity of a cellbattery pack 205. The chargeable capacity of the cell may be computedbased on SOC of the cell, capacity of the cell, current flowing throughthe cell, and current flowing in all branches of the module in which thecell is located. The value of the chargeable capacity of the cell islowest amongst the values of chargeable capacities of a plurality ofbattery cells in the plurality of branches of each of the plurality ofmodules.

FIG. 2 illustrates various example units of the BMS 200, but it is to beunderstood that other embodiments are not so limited. In otherembodiments, the BMS 200 may include less or more number of units.Further, the labels or names of the units of the BMS 200 are used simplyfor illustrative purposes and do not limit the scope of the disclosure.One or more units can be combined together to perform same orsubstantially similar function in the BMS 200.

FIG. 3 is a flowchart 300 illustrating an example method for estimatingcapacity and SOC of the battery pack 205 based on variations ofparameters pertaining to battery cells of the battery pack 205,according to various embodiments. At operation 301, the method includesdetermining at least one value of at least one parameter pertaining toeach of a plurality of battery cells in the battery pack 205. The atleast one parameter pertaining to a battery cell, among the plurality ofbattery cells, includes, for example, and without limitation, SOC of thebattery cell, capacity of the battery cell, voltage of the battery cell,current flowing through the battery cell, ambient temperature of thebattery cell, surface temperature of the battery cell, etc. Variousembodiments include determining the at least one parameter pertaining toa battery cell based on operating current fed to the battery pack 205,at least one electrochemical parameter fed to the battery pack 205, atleast one thermal parameter fed to the battery pack 205, internalresistance of the battery cell, and connection resistance of the batterycell.

In an embodiment, the at least one parameter may be determined using amodel, including a plurality of fully coupled models. The sub-models mayinclude, for example, and without limitation, an equivalent circuitmodel, an electrochemical model, and a thermal model. The sub-models canreceive, as inputs, the operating current fed to the battery pack 205,the at least one electrochemical parameter, the at least one thermalparameter, the internal resistances of the battery cells of the batterypack 205, and connection resistances of the battery cells battery pack205. The sub-models may determine the at least one value of the at leastone parameter (operating current fed to the battery pack 205, the atleast one electrochemical parameter, the at least one thermal parameter,internal resistance of the battery cell, and connection resistance ofthe battery cell) pertaining to each of a plurality of battery cells inthe battery pack 205 based on the inputs.

The sub-models of the model may be coupled based on inputs and outputsexchanged between the sub-models. A first parameter generated as anoutput by a first sub-model may be used by a second sub-model as aninput. A second parameter generated as an output by the second sub-modelmay be used by the first sub-model as an input. For example, theequivalent circuit model may receive the voltage of the individualcells, from the electrochemical model. The electrochemical model mayreceive the current flowing through the individual cells from theequivalent circuit model, and ambient temperature from the thermalmodel, as inputs. The thermal model may receive the surface temperatureof the individual cells from the electrochemical model as an input.

At operation 302, the example method includes computing at least one ofan uptime of the battery pack 205, a remaining capacity of the batterypack 205, a chargeable capacity of the battery pack 205, and an SOC ofthe battery pack 205 based on variations in the at least one parameteramong the plurality of battery cells in the battery pack. Consider thatthe battery pack comprises a plurality of modules connected in series.Each of the plurality of modules may include a plurality of branchesconnected in parallel, wherein each of the plurality of branchescomprises a battery cell. Various embodiments include determining atleast one of SOC, capacity, voltage, current, and ambient and surfacetemperatures, of each of the battery cells in the plurality of branchesof each of the plurality of modules, using the model.

Once the parameters (SOC, capacity, voltage, current, ambienttemperature, and surface temperature) pertaining to each of the batterycells have been determined using the model, various embodiments includecomputing the uptime of the battery pack 205, the remaining capacity ofthe battery pack 205, the chargeable capacity of the battery pack 205,and the SOC of the battery pack.

The uptime of the battery pack 205 may be the uptime of a battery cellin a branch of a module. For a particular branch in a module, variousembodiments include computing a product of capacity of the battery celland SOC of the battery cell. Various embodiments include obtaining aratio of the product and the current flowing through the battery cell.Various embodiments include computing the ratios for each of the batterycells in each of the branches of the module. The ratio with the lowestvalue can be considered as the uptime of the module. Similarly, variousembodiments include computing the uptimes of each of the plurality ofmodules. The lowest value of uptime, among the values of the uptimes ofeach of the plurality of modules, is considered as the uptime of thebattery pack 205.

The remaining capacity of the battery pack 205 may be the remainingcapacity of a battery cell in a branch of a module. For a particularbranch in a module, various embodiments include computing a product ofthe uptime of the battery cell in the branch and the summation ofcurrents in each of the plurality of branches in the module. Variousembodiments include computing the products for each of the plurality ofbranches in the module. The values of the products represent theremaining capacities of the battery cells in the plurality of branchesof the module. The product with the lowest value can be considered asthe remaining capacity of the module. Similarly, various embodimentsinclude determining the remaining capacities of each of the plurality ofmodules. The lowest value of remaining capacity, amongst the values ofthe remaining capacities of each of the plurality of modules, isconsidered as the remaining capacity of the battery pack 205.

The chargeable capacity of the battery pack 205 may be the chargeablecapacity of a battery cell in a branch of a module. For a particularbranch in a module, various embodiments include computing a ratio ofcapacity of the battery cell in the branch and the current passingthrough the branch. Various embodiments include computing a differencebetween the ratio and the uptime of the battery cell in the branch.Various embodiments include computing a product of the difference andthe summation of currents in each of the plurality of branches in themodule. Similarly, various embodiments include computing the productsfor each of the plurality of branches in the module. The values of theproducts represent the chargeable capacities of the battery cells in theplurality of branches of the module. The product with the lowest valuecan be considered as the chargeable capacity of the module. Similarly,various embodiments include determining the chargeable capacities ofeach of the plurality of modules. The lowest value of chargeablecapacity, among the values of the chargeable capacities of each of theplurality of modules, is considered as the chargeable capacity of thebattery pack 205.

The SOC of the battery pack 205 may be determined based on a ratio ofthe remaining capacity of the battery pack 205 and the original capacityof the battery pack 205.

The various actions in the flowchart 300 may be performed in the orderpresented, in a different order, or simultaneously. Further, in someembodiments, some actions listed in FIG. 3 may be omitted.

FIG. 4 is a diagram illustrating an example model for estimation ofparameters pertaining to the individual cells of the battery pack 205,according to various embodiments. As illustrated in FIG. 4 , the modelmay include three sub-models, including, for example, an electricalequivalent circuit model, a convective thermal model, and a cell reducedorder electrochemical-thermal model. The model may, for example, beconfigured to estimate the SOC of each of the individual cells, thecapacity of each of the individual cells, the voltage drop across theterminals of each of the individual cells, the current flowing througheach of the individual cells, and the ambient and surface temperaturesof each of the individual cells.

The model may receive the applied current (I_(app)) or operatingcurrent, electrochemical parameters, thermal parameters, internalresistances of each of the individual cells, and connection resistancesof each of the individual cells, as inputs. The electrical equivalentcircuit model receives the applied current, the internal resistances andthe connection resistances of each of the individual cells. The cellreduced order electrochemical-thermal model receives the electrochemicalparameters. The convective thermal model receives the thermal parametersas input.

The sub-models, e.g., the electrical equivalent circuit model, theconvective thermal model, and the cell reduced orderelectrochemical-thermal model are coupled with each other. The couplingmay be based on a first sub-model receiving an input from a secondsub-model, to generate an output. The generated output is received bythe second sub-model to generate an output. For example, the electricalequivalent circuit model receives the voltage (φ_(jk)) of a cell(cell-jk) from the cell reduced order electrochemical-thermal model, asinput. The cell reduced order electrochemical-thermal model receives thecurrent flowing through the cell-jk (i_(jk)) from the electricalequivalent circuit model, and the ambient temperature (T_(amb)) of thecell-jk from the convective thermal model, as inputs. The cell reducedorder electrochemical-thermal model generates the capacity and the SOC.The convective thermal model receives the surface temperature (T_(jk))of the cell-jk from the cell reduced order electrochemical-thermal modelas an input.

Based on the estimates of the SOC, capacity, voltage, current, andambient and surface temperatures, of the individual cells of the batterypack 205, derived by the model, various embodiments include determiningthe uptime of the battery pack 205, the SOC of the battery pack 205, theremaining capacity of the battery pack 205, and the chargeable capacityof the battery pack 205.

FIG. 5 is a diagram illustrating an example battery pack comprising ofthree modules, wherein each of the three modules comprises two branches,according to various embodiments. As illustrated in FIG. 5 , each branchof a module includes a cell. As there are three modules in the batterypack and two branches in each module, the cells in the first module canbe labeled as Cell-1-1 and Cell-1-2. Similarly, the cells in the secondmodule can be labeled as Cell-2-1 and Cell-2-2, and the cells in thethird module can be labeled as Cell-3-1 and Cell-3-2. The resistances ofthe cells in the first module are labeled as r₁₁ and r₁₂. Theresistances of the cells in the second module are labeled as r₂₁ andr₂₂. The resistances of the cells in the third module are labeled as r₃₁and r₃₂.

The battery pack model may determine variations in temperature, SOC,capacity, internal resistance, busbar resistance, voltage, and current,amongst the six cells in six branches of the three modules of batterypack. The battery pack model determines the currents flowing through thetwo branches of each of the three modules. The currents are labeled asi₁₁, i₁₂, i₂₁, i₂₂, i₃₁, and i₃₂. The battery pack model may determinethe uptime of the battery pack, the remaining capacity of the batterypack, the chargeable capacity of the battery pack, and the SOC of thebattery pack; based on variations in the temperature, SOC, capacity,internal resistance, busbar resistance, voltage, and current, amongstthe six cells in six branches of the three modules of battery pack.

The uptime of the battery pack is given as:

${{Uptime}\underset{1 \leq j \leq 3}{({pack})}} = {\min\left\{ {\min\limits_{1 \leq k \leq 2}\left( \frac{SOC_{jk}Q_{jk}}{i_{jk}} \right)} \right\}}$

The remaining capacity of the battery pack is given as:

${{Rem}{{Cap}({pack})}} = {\min\limits_{1 \leq j \leq 3}\left\{ {{\min\limits_{1 \leq k \leq 2}\left( \frac{SOC_{jk}Q_{jk}}{i_{jk}} \right)}\left( {\sum\limits_{k = 1}^{2}i_{jk}} \right)} \right\}}$

The chargeable capacity of the battery pack is given as:

${{Crg}{{Cap}({pack})}} = {\min\limits_{1 \leq j \leq 3}\left\{ {{\min\limits_{1 \leq k \leq 2}\left( \frac{1 - {SOC_{jk}}}{i_{jk}} \right)}{Q_{jk}\left( {\sum\limits_{k = 1}^{2}i_{jk}} \right)}} \right\}}$

The SOC of the battery pack is determined based on the remainingcapacity of the battery pack and the total capacity of the battery pack.The SOC of the battery pack is given as:

${So{C({pack})}} = \frac{\min\limits_{1 \leq j \leq 3}\left\{ {{\min\limits_{1 \leq k \leq 2}\left( \frac{SOC_{jk}Q_{jk}}{i_{jk}} \right)}\left( {\sum\limits_{k = 1}^{2}i_{jk}} \right)} \right\}}{Q_{pack}^{d}}$

Various embodiments disclosed herein can be implemented through at leastone software program running on at least one hardware device andperforming network management functions to control the network elements.The network elements shown in FIG. 2 include blocks which can be atleast one of a hardware device, or a combination of hardware device andsoftware module.

Various example embodiments disclosed herein describe methods andsystems for providing a model for accurately estimating battery packuptime, remaining capacity of the battery pack available for discharge,and chargeable capacity of the battery pack. Therefore, it is understoodthat the scope of the disclosure is extended to such a program and inaddition to a computer readable medium having a message therein, suchcomputer readable storage medium may contain program code forimplementation of one or more steps of the method, when the program runson a server or mobile device or any suitable programmable device. Themethod may be implemented in example embodiment through or together witha software program written in example Very high speed integrated circuitHardware Description Language (VHDL), or any other programming language,or implemented by one or more VHDL or several software modules beingexecuted on at least one hardware device. The hardware device can be anykind of portable device that can be programmed. The device may alsoinclude hardware, for example, an Application-specific IntegratedCircuit (ASIC), or a combination of hardware and software, for example,an ASIC and a Field Programmable Gate Array (FPGA), and/or at least onemicroprocessor and at least one memory with software modules locatedtherein. The various example embodiments described herein may beimplemented partly in hardware and partly in software. Variousembodiments may be implemented on different hardware devices, e.g. usinga plurality of Central Processing Units (CPUs).

The foregoing description of various example embodiments discloses thevarious embodiments herein so that others can, by applying currentknowledge, readily modify and/or adapt for various applications suchvarious embodiments without departing from the concept, and, therefore,such adaptations and modifications should and are intended to becomprehended within the meaning and range of equivalents of thedisclosed embodiments. It is to be understood that the phraseology orterminology employed herein is for the purpose of description and not oflimitation. Therefore, while various example embodiments herein havebeen described in terms of example embodiments, those skilled in the artwill recognize that the various example embodiments herein can bepracticed with modification within the scope of the embodiments asdescribed herein.

What is claimed is:
 1. A method for obtaining information on a batterypack by an electronic device, the method comprising: identifying, by theelectronic device, at least one value of at least one parameterpertaining to each of a plurality of battery cells in the battery pack;and obtaining, by the electronic device, at least one of an uptime ofthe battery pack, a remaining capacity of the battery pack and achargeable capacity of the battery pack, based on variations in the atleast one value of the at least one parameter among the plurality ofbattery cells in the battery pack, wherein the at least one parameterpertaining to a battery cell, among the plurality of battery cells,comprises a State of Charge (SOC) of the battery cell, capacity of thebattery cell, and current flowing through the battery cell, wherein theuptime of the battery pack includes an uptime of a battery cell in abranch of a module, wherein a value of the uptime of the battery cell islowest among values of uptimes of a plurality of battery cells in aplurality of branches of each of a plurality of modules, wherein thevalue of the uptime of the battery cell is based on the SOC of thebattery cell, capacity of the battery cell, and current flowing throughthe battery cell.
 2. The method, as claimed in claim 1, wherein the atleast one value of the at least one parameter is identified, by theelectronic device, using a model, wherein the model comprises anequivalent circuit model, an electrochemical model, and a thermal model,wherein the equivalent circuit model, the electrochemical model, and thethermal model are coupled.
 3. The method, as claimed in claim 1, whereinthe at least one parameter pertaining to the battery cell, among theplurality of battery cells further comprises voltage drop acrossterminals of the battery cell, ambient temperature of the battery cell,and surface temperature of the battery cell.
 4. The method, as claimedin claim 1, wherein the at least one value of the at least one parameterpertaining to a battery cell, among the plurality of battery cells, isidentified based on at least one of operating current fed to the batterypack, at least one electrochemical parameter fed to the battery pack, atleast one thermal parameter fed to the battery pack, internal resistanceof the battery cell, and connection resistance of the battery cell. 5.The method, as claimed in claim 1, wherein the battery pack comprisesthe plurality of modules connected in series, wherein each of theplurality of modules comprises a plurality of branches connected inparallel, wherein each of the plurality of branches comprises a batterycell.
 6. The method, as claimed in claim 3, wherein the remainingcapacity of the battery pack includes a remaining capacity of a batterycell in a branch of a module, wherein a value of the remaining capacityof the battery cell is lowest among values of remaining capacities of aplurality of battery cells in the plurality of branches of each of theplurality of modules, wherein the value of the remaining capacity of thebattery cell is based on the SOC of the battery cell, capacity of thebattery cell, current flowing through the battery cell, and currentflowing in all branches of the module.
 7. The method, as claimed inclaim 3, wherein the chargeable capacity of the battery pack includes achargeable capacity of a battery cell in a branch of a module, whereinvalue of the chargeable capacity of the battery cell is lowest amongvalues of chargeable capacities of a plurality of battery cells in theplurality of branches of each of the plurality of modules, wherein thevalue of the chargeable capacity of the battery cell is based on the SOCof the battery cell, capacity of the battery cell, current flowingthrough the battery cell, and current flowing in all branches of themodule.
 8. The method, as claimed in claim 1, wherein the method furthercomprises computing, by the electronic device, a State of Charge (SOC)of the battery pack, based on the remaining capacity of the battery packand a total capacity of the battery pack.
 9. An electronic devicecomprising: a battery pack; and at least one processor configured to:identify at least one value of at least one parameter pertaining to eachof a plurality of battery cells in the battery pack; and obtain at leastone of an uptime of the battery pack, a remaining capacity of thebattery pack and a chargeable capacity of the battery pack, based onvariations in the at least one value of the at least one parameter amongthe plurality of battery cells in the battery pack, wherein the at leastone parameter pertaining to a battery cell, among the plurality ofbattery cells comprises a State of Charge (SOC) of the battery cell,capacity of the battery cell, and current flowing through the batterycell, wherein the uptime of the battery pack includes an uptime of abattery cell in a branch of a module, wherein a value of the uptime ofthe battery cell is lowest among values of uptimes of a plurality ofbattery cells in a plurality of branches of each of a plurality ofmodules, wherein the value of the uptime of the battery cell is based onthe SOC of the battery cell, capacity of the battery cell, and currentflowing through the battery.
 10. The electronic device as claimed inclaim 9, wherein the at least one value of the at least one parameter isidentified, by the at least one processor, using a model, wherein themodel comprises an equivalent circuit model, an electrochemical model,and a thermal model, wherein the equivalent circuit model, theelectrochemical model, and the thermal model are coupled.
 11. Theelectronic device as claimed in claim 9, wherein the at least oneparameter pertaining to the battery cell, among the plurality of batterycells comprises voltage drop across terminals of the battery cell,ambient temperature of the battery cell, and surface temperature of thebattery cell.
 12. The electronic device as claimed in claim 9, whereinthe at least one value of the at least one parameter pertaining to abattery cell, among the plurality of battery cells, is determined basedon at least one of operating current fed to the battery pack, at leastone electrochemical parameter fed to the battery pack, at least onethermal parameter fed to the battery pack, internal resistance of thebattery cell, and connection resistance of the battery cell.
 13. Theelectronic device as claimed in claim 9, wherein the battery packcomprises the plurality of modules connected in series, wherein each ofthe plurality of modules comprises a plurality of branches connected inparallel, wherein each of the plurality of branches comprises a batterycell.
 14. The electronic device as claimed in claim 11, wherein theremaining capacity of the battery pack includes a remaining capacity ofa battery cell in a branch of a module, wherein a value of the remainingcapacity of the battery cell is lowest among values of remainingcapacities of a plurality of battery cells in the plurality of branchesof each of the plurality of modules, wherein the value of the remainingcapacity of the battery cell is based on the SOC of the battery cell,capacity of the battery cell, current flowing through the battery cell,and current flowing in all branches of the module.
 15. The electronicdevice as claimed in claim 11, wherein the chargeable capacity of thebattery pack includes a chargeable capacity of a battery cell in abranch of a module, wherein value of the chargeable capacity of thebattery cell is lowest among values of chargeable capacities of aplurality of battery cells in the plurality of branches of each of theplurality of modules, wherein the value of the chargeable capacity ofthe battery cell is based on the SOC of the battery cell, capacity ofthe battery cell, current flowing through the battery cell, and currentflowing in all branches of the module.
 16. The electronic device asclaimed in claim 9, wherein the at least one processor is furtherconfigured to compute a State of Charge (SOC) of the battery pack, basedon the remaining capacity of the battery pack and a total capacity ofthe battery pack.